Check out your local library. Many of them offer mom-and-me story time and/or craft classes and they are typically free of charge. We did a lot of library programs when my two where toddlers. :)
Try your community or county parks department. They also often run programs that, while not free, tend to be cheap. I know the county system in my area does single session themed project and learning programs for $5 per kid. Some programs can run a bit more but it's rarely a lot more.
I'm not sure if you've got a religious affiliation or not, but poke around the area churches. Many in my area host toddler/preschooler playgroups open to the community. Some do have a bit of Bible story component, but mostly it' just play and fun time. Look for moms' groups in your area - they will at least offer organized playgroup dates and gatherings. I found one in my town by googling "[city name] mom group" and "[city] playgroup."
at 11:51 AM on Jan. 11, 2011